Details

sample156.0ms

Algorithm

intervals

Results

44.0ms	265×	body	80	valid
29.0ms	26×	body	1280	valid
18.0ms	25×	body	640	valid
17.0ms	14×	body	160	valid
15.0ms	28×	body	320	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
1.8b	(cos (/ (+ phi2 phi1) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
20.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
25.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
9.0ms	(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

507.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
662.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
154.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
38.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4185
2	1076
1	360
0	144

prune598.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
1.8b	(cos (* 1/2 (+ phi1 phi2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `hypot-udef` `distribute-lft-in` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
37.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
9.0ms	(cos (* 1/2 (+ phi1 phi2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

601.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
719.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
138.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
31.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify2.4s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4384
2	1076
1	377
0	158

prune636.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)
0.1b	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
0.2b	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
0.2b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`flip3--` `associate-r` `flip--` `sin-mult`
8×	`frac-times` `cos-mult`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `insert-posit16` `log1p-expm1-u` `sub-div`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/`
1×	`fma-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

13.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)
79.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
332.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
56.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

series21.5s

Counts

4 → 12

Calls

4 calls:

21.0s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))) (- phi1 phi2)) R)
121.0ms	(- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
331.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
106.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))

simplify5.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5004
2	3452
1	885
0	318

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.2b	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
0.2b	(* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
26.6b	(cbrt (* (* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
18×	`sin-mult`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-div` `associate-r` `associate-l`
6×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`cbrt-prod` `pow2` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube`

Counts

4 → 104

Calls

4 calls:

28.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
28.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
203.0ms	(* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
348.0ms	(cbrt (* (* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
81.0ms	(* (sin (* phi1 1/2)) (sin (* phi2 1/2)))
120.0ms	(* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2))))
92.0ms	(cbrt (* (* (* (sin (* phi1 1/2)) (sin (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1104
1	293
0	125

prune937.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes754.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.2s	8526×	body	80	valid
956.0ms	1269×	body	640	valid
892.0ms	794×	body	1280	valid
488.0ms	738×	body	320	valid
186.0ms	330×	body	160	valid